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Vortex Properties from Resistive Transport Measurements on Extreme Type-II Superconductors

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Vortex Properties from Resistive Transport Measurements on Extreme Type-II Superconductors Vortex Properties from Resistive Transport Measurements on Extreme Type-II Superconductors Andreas Rydh Stockholm 2001 Doctoral Dissertation Solid State Physics Dept. of Physics & Dept. of Electronics Royal Institute of Technology (KTH) Typeset in LATEX. BIBTEX and the natbib package were used for the bibliography. Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan framlägges till offentlig granskning för avläggande av teknisk doktorsexamen fredagen den 25 januari 2002 kl 10.00 i Kollegiesalen, Administrationsbyggnaden, Kungl Tekniska Högskolan, Valhallavägen 79, Stockholm. Thesis for the degree of Ph. D. in the subject area of Condensed Matter Physics. TRITA-FYS-5275 ISSN 0280-316X ISRN KTH/FYS/FTF/R--01/5275--SE ISBN 91-7283-175-8 Copyright © Andreas Rydh, 2001 Printed in Sweden by Universitetsservice US AB, Stockholm Vortex Properties from Resistive Transport Measurements on Extreme Type-II Superconductors Andreas Rydh, Solid State Physics, Royal Institute of Technology (KTH), Stockholm, Sweden Abstract The nature of vortices in extreme type-II superconductors has been an ever growing field of Ì research all since the discovery of the first high- materials in 1986. This thesis focuses on the study of vortex phase transitions and vortex-liquid properties through resistive trans- ¿ Æ port measurements on single crystals of mainly YBa ¾ Cu O (YBCO). Some important results are the following: (i) Location of the vortex glass transition. A study of the second-order vortex glass tran- Ì sition in the magnetic field–temperature (À – ) phase diagram as a function of anisotropy « ¾ ­ À ´Ì µ » ­ ´½ ÌÌ µ´ÌÌ µ resulted in a simple description of the glass line, ´À Ì µ Ì « over an extended region. Here is the critical temperature, is a parameter, and À . No evidence was found for any 3D–2D transition in the studied range of field and À ½¾ ­ ¿ anisotropy ( ¼ T, ). (ii) Description of the vortex-liquid resistivity in glassy systems. By introducing a mod- ´À Ì µ ified vortex-glass correlation length , depending on a mean local pinning energy Í ´À Ì µ Ì ¼ and the thermal energy , an explicit description of the vortex-liquid resis- Ì tivity close to the second-order phase transition was obtained both for varying À and . (iii) Driven vortex dynamics in clean systems. The vortex-solid dynamics below the first- Ì ´À µ order melting transition Ñ was found to be divided into a flux-creep region with high critical current density at low temperatures, and an almost Ohmic flux-flow regime with low . (iv) Vortex-liquid correlation and multiterminal measurements. Using various multiter- Ì minal setups, the vortex liquid in YBCO just above Ñ was shown to be rather strongly correlated along the vortex line also in untwinned crystals. The longitudinal and transversal resistivities and their mutual relation were investigated. (v) In-plane anisotropy of YBCO. A new multiterminal configuration allowed measure- ments of the in-plane anisotropy as a function of temperature and magnetic field direction. The measurements revealed a possible presence of nearly isotropic fluctuations, corre- ­ ½½ sponding to a fluctuation anisotropy ­ . This value is clearly lower than that ­ ½¿ obtained from the vortex phase diagram or from resistive measurements, . Ì The thesis starts with a short overview, followed by an introduction to vortices in high- and subsequent discussions of various vortex properties. The published papers are shortly summarized and are finally appended. ¾ ¿ ¿ Æ Keywords: superconductivity, vortex, phase transition, YBa Cu O , (K,Ba)BiO , vortex dynamics, critical current, single crystal, oxygen deficiency, anisotropy, vortex glass, vortex lattice, melting, vortex liquid, vortex correlation, disorder, Lorentz force. ¯ ¯ ISBN 91-7283-175-8 ¯ TRITA-FYS-5275 ISSN 0280-316X ISRN KTH/FYS/FTF/R--01/5275--SE iii Vortexegenskaper från resistiva transportmätningar på extrema typ-II-supraledare Andreas Rydh, Fasta Tillståndets Fysik, Kungliga Tekniska Högskolan, Stockholm Sammanfattning Vortexars egenskaper i extrema typ-II-supraledare har varit ett ständigt växande forsk- Ì ningsområde alltsedan upptäckten av de första hög- materialen år 1986. Denna av- handling är fokuserad på studiet av fasomvandlingar i vortexsystemet och på vortexväts- kans egenskaper. Den experimentella metod som använts är resistiva transportmätningar ¿ Æ på enkristaller av huvudsakligen YBa ¾ Cu O (YBCO). Några viktiga resultat beskrivs kortfattat: (i) Läget hos vortexglasövergången. En studie av den andra ordnings fasomvandling som här tolkas som en vortexglasövergång i fasdiagrammet över magnetfält mot temperatur « ¾ À Ì À ´Ì µ » ­ ´½ ÌÌ µ´ÌÌ µ ( – ), ledde till en enkel beskrivning av glaslinjen, , ´À Ì µ ­ Ì « över ett utökat område. Här är anisotropin, den kritiska temperaturen, en parameter och À . Inga tecken på någon 3D–2D övergång kunde observeras i det À ½¾ ­ ¿ studerade området av fält och anisotropi ( ¼ T, ). (ii) Beskrivning av vortexvätskans resistivitet i glasliknande system. Genom att introdu- ´À Ì µ cera en modifierad vortexglas-korrelationslängd , bestämd av ett medelvärde av Í ´À Ì µ Ì den lokala pinningenergin ¼ och den termiska energin , så erhölls en explicit Ì beskrivning av vortexvätskans resistivitet både för varierande À och i närheten av andra ordningens fasomvandling. (iii) Vortexdynamik i rena system vid hög ström. En fasomvandling av första ordningen Ì ´À µ inträffar i vortexsystemet vid en smälttemperatur Ñ . Dynamiken hos den fasta vortex- fas som uppträder under denna fasomvandling befanns vara uppdelad i ett fluxkrypområde med hög kritisk strömtäthet vid låga temperaturer och ett nästan Ohmskt vortexflödes- område med lågt . (iv) Vortexvätskekorrelation och multikontaktmätningar. Genom att använda olika kon- Ì figurationer med många kontakter så visades att vortexvätskan i YBCO precis ovanför Ñ är ganska starkt korrelerad längs med vortexlinjen även i otvinnade kristaller. De longitu- dinella och transversella resistiviteterna och deras ömsesidiga relation undersöktes. (v) Anisotropin i planet hos YBCO. En ny kontaktkonfiguration möjliggjorde multikon- taktmätningar av anisotropin i planet som funktion av temperatur och magnetfältsriktning. Mätresultaten indikerade en möjlig närvaro av nästan isotropa fluktuationer, motsvarande ­ ½½ en fluktuationsanisotropi ­ . Detta värde är klart lägre än det som erhålls från ­ ½¿ vortexfasdiagrammet eller från resistiva mätningar, . Avhandlingen inleds med en kort översikt, följd av en introduktion till vortexar i hög- Ì och en efterföljande diskussion av olika vortexegenskaper. De publicerade artiklarna sammanfattas kort och är slutligen bifogade. ¾ ¿ ¿ Æ Nyckelord: supraledning, vortex, fasomvandling, YBa Cu O , (K,Ba)BiO , vortexdynamik, kritisk ström- täthet, enkristall, syredopning, anisotropi, vortexglas, vortexgitter, smältning, vortexvätska, vortexkorrelation, oordning, Lorentzkraft. ¯ ¯ ISBN 91-7283-175-8 ¯ TRITA-FYS-5275 ISSN 0280-316X ISRN KTH/FYS/FTF/R--01/5275--SE iv Preface This thesis is based on my research within the Solid State Physics group at the Royal Institute of Technology, Stockholm, during the period 1997–2001. It consists of two parts. The first part of the thesis is intended to assist the reader to become acquainted with the language of vortices and superconductivity and to describe the context of the present work in the vast current efforts in vortex physics. After a brief overview I continue with introducing some basic concepts of superconductivity and the central role of anisotropy, before discussing various vortex properties and how they can be studied through transport measurements. The short overview is aimed at readers with a basic knowledge in supercon- ductivity, so the inexperienced reader may prefer to begin the reading with the introduction to superconductivity (page 4). The second part consists of the publications, which compose the main part of the thesis. Some results are also found in the introductory part, while others are presented only in the papers. List of publications The following papers are included in the thesis: ¿ Æ I. Vortex dynamics in oxygen deficient single crystals of YBa ¾ Cu O B. Lundqvist, A. Rydh, Ö. Rapp, and M. Andersson, Physica (Amsterdam) 282–287 C, 1959 (1997). Ì II. Empirical scaling of the vortex glass line above 1 T for high- super- conductors of varying anisotropy B. Lundqvist, A. Rydh, Yu. Eltsev, Ö. Rapp, and M. Andersson, Phys. Rev. B 57, R 14 064 (1998). Ì III. Consistent description of the vortex glass resistivity in high- super- conductors A. Rydh, Ö. Rapp, and M. Andersson, Phys. Rev. Lett. 83, 1850 (1999). IV. Thermally assisted flux creep of a driven vortex lattice in untwinned ¿ Æ YBa¾ Cu O single crystals A. Rydh, M. Andersson, and Ö. Rapp, J. Low Temp. Phys. 117, 1335 (1999). V. Magnetic field scaling of the vortex glass resistivity in oxygen deficient ¿ Æ YBa¾ Cu O single crystals A. Rydh, Ö. Rapp, and M. Andersson, Physica (Amsterdam) 284–288 B, 707 (2000). v vi List of publications VI. Multiterminal measurements of vortex correlations in the (K,Ba)BiO ¿ system A. Rydh, T. Klein, I. Joumard, and Ö. Rapp, Physica (Amsterdam) 341–348 C, 1233 (2000). ¿ Æ VII. Vortex liquid resistivity in disordered YBa ¾ Cu O single crystals M. Andersson, A. Rydh, and Ö. Rapp, Physica (Amsterdam) 341–348 C, 1239 (2000). VIII. Strong vortex liquid correlation from multiterminal measurements on ¿ Æ untwinned YBa¾ Cu O single crystals A. Rydh and Ö. Rapp, Phys. Rev. Lett. 86, 1873 (2001). IX. Scaling of
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